Preparation: Copy
the chart below on a piece of paper on a piece of paper.

How
To Perform: Tell your friend that you are
going to make a prediction. Write down
the following on a piece of paper without letting them see what you are writing:

The
sum of the four numbers you choose will be 34!

Fold the prediction up a few
times and set it aside. Hand your friend the chart you
made. Tell them to circle any number on
the chart. See example below.

Next have then cross off all of
the numbers in the same column and row of the number that they circled. See
below.

Now
ask them to circle any number on the
chart that is not circled or crossed out.
After they circle their number, have them repeat the same process as
before (cross off all of the numbers in the same column and row of the number
that they circled.)

Then
tell them to repeat these same directions until they have four numbers circled
and all other numbers are crossed out.
After they circle the fourth number, there should be no more numbers to
cross out.

Now they just have one more number left to circle and then we are ready for the grand finale!

Have
them add together the four numbers that are circled and announce the total to
you. Next unfold the paper that was
placed aside to reveal the prediction. It will always match their total!

Secret: Let's see why this trick works. Anytime you have a square array of consecutive numbers, the sum of the four circled numbers will always be the sum of either of the diagonals.

So for our example above, the numbers for one of the diagonals is 1, 6, 11, and 16. Let's add these numbers up:

1 + 6 + 11 + 16 = 34

The numbers for the other diagonal are 4, 7, 10, and 13. Adding these gives:

4 + 7 + 10 + 13 = 34

So there's really no need to add up both diagonals.

If your friend wants you to repeat the trick

Usually people want to see a trick more than once. So the second time I perform the trick, I use a different number chart so the prediction number will not be the same. The number chart below can be used to perform the trick a second time.

The prediction sum for this set of numbers will be 65. Just add up either diagonal and the sum is 65. And there you have it, another cool math trick to amaze friends and family!